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Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing

Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing

Egorova, V.N., Tan, S. H., Lai, Ci-H., Company, R. and Jodar, L. (2015) Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing. International Journal of Computer Mathematics, 94 (2). pp. 345-362. ISSN 0020-7160 (Print), 1029-0265 (Online) (doi:10.1080/00207160.2015.1108409)

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Abstract

The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden’s and Schubert’s methods are applied as a modification to Newton’s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods.

Item Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis Group in International Journal of Computer Mathematics, in Dec 2015, available online: http://www.tandfonline.com/10.1080/00207160.2015.1108409
Uncontrolled Keywords: Nonlinear PDE, Free boundary, Transformation, Finite difference methods, Newton-like method, Alternating direction explicit method
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 01 May 2018 14:06
Selected for GREAT 2016: GREAT b
Selected for GREAT 2017: None
Selected for GREAT 2018: GREAT a
URI: http://gala.gre.ac.uk/id/eprint/14893

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